{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.ticker import LinearLocator, FormatStrFormatter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def z_func(x, y):\n",
    "    return ((x**2 + y**2)/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(-3.0, 3.0, 0.1)\n",
    "y = np.arange(-3.0, 3.0, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X,Y = np.meshgrid(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = z_func(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, Y, Z, rstride = 1, cstride = 1,\n",
    "                      cmap = cm.RdBu, linewidth = 0, antialiased = False)\n",
    "ax.zaxis.set_major_locator(LinearLocator(10))\n",
    "ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
    "fig.colorbar(surf, shrink = 0.5, aspect = 5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "epoch = 10000\n",
    "x = -3\n",
    "prev_x = 0\n",
    "y = 2\n",
    "prev_y =0\n",
    "r = 0.01\n",
    "precision = 0.00001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iterator 0 with x: -2.97,y : 1.98\n",
      "iterator 1 with x: -2.9403,y : 1.9602\n",
      "iterator 2 with x: -2.9108970000000003,y : 1.940598\n",
      "iterator 3 with x: -2.8817880300000005,y : 1.9211920200000001\n",
      "iterator 4 with x: -2.8529701497000004,y : 1.9019800998\n",
      "iterator 5 with x: -2.8244404482030006,y : 1.882960298802\n",
      "iterator 6 with x: -2.7961960437209705,y : 1.86413069581398\n",
      "iterator 7 with x: -2.768234083283761,y : 1.8454893888558404\n",
      "iterator 8 with x: -2.7405517424509234,y : 1.8270344949672819\n",
      "iterator 9 with x: -2.713146225026414,y : 1.808764150017609\n",
      "iterator 10 with x: -2.68601476277615,y : 1.790676508517433\n",
      "iterator 11 with x: -2.6591546151483882,y : 1.7727697434322587\n",
      "iterator 12 with x: -2.6325630689969044,y : 1.7550420459979361\n",
      "iterator 13 with x: -2.6062374383069353,y : 1.7374916255379567\n",
      "iterator 14 with x: -2.580175063923866,y : 1.720116709282577\n",
      "iterator 15 with x: -2.554373313284627,y : 1.7029155421897513\n",
      "iterator 16 with x: -2.528829580151781,y : 1.6858863867678537\n",
      "iterator 17 with x: -2.503541284350263,y : 1.6690275229001752\n",
      "iterator 18 with x: -2.4785058715067607,y : 1.6523372476711735\n",
      "iterator 19 with x: -2.453720812791693,y : 1.6358138751944618\n",
      "iterator 20 with x: -2.429183604663776,y : 1.619455736442517\n",
      "iterator 21 with x: -2.404891768617138,y : 1.603261179078092\n",
      "iterator 22 with x: -2.3808428509309665,y : 1.587228567287311\n",
      "iterator 23 with x: -2.357034422421657,y : 1.571356281614438\n",
      "iterator 24 with x: -2.3334640781974403,y : 1.5556427187982935\n",
      "iterator 25 with x: -2.310129437415466,y : 1.5400862916103106\n",
      "iterator 26 with x: -2.287028143041311,y : 1.5246854286942075\n",
      "iterator 27 with x: -2.264157861610898,y : 1.5094385744072654\n",
      "iterator 28 with x: -2.241516282994789,y : 1.4943441886631927\n",
      "iterator 29 with x: -2.2191011201648414,y : 1.4794007467765609\n",
      "iterator 30 with x: -2.196910108963193,y : 1.4646067393087951\n",
      "iterator 31 with x: -2.174941007873561,y : 1.4499606719157072\n",
      "iterator 32 with x: -2.1531915977948253,y : 1.43546106519655\n",
      "iterator 33 with x: -2.131659681816877,y : 1.4211064545445846\n",
      "iterator 34 with x: -2.1103430849987084,y : 1.4068953899991388\n",
      "iterator 35 with x: -2.0892396541487215,y : 1.3928264360991474\n",
      "iterator 36 with x: -2.0683472576072344,y : 1.3788981717381559\n",
      "iterator 37 with x: -2.047663785031162,y : 1.3651091900207744\n",
      "iterator 38 with x: -2.0271871471808502,y : 1.3514580981205666\n",
      "iterator 39 with x: -2.0069152757090416,y : 1.337943517139361\n",
      "iterator 40 with x: -1.9868461229519512,y : 1.3245640819679674\n",
      "iterator 41 with x: -1.9669776617224317,y : 1.3113184411482877\n",
      "iterator 42 with x: -1.9473078851052075,y : 1.2982052567368048\n",
      "iterator 43 with x: -1.9278348062541555,y : 1.2852232041694367\n",
      "iterator 44 with x: -1.908556458191614,y : 1.2723709721277423\n",
      "iterator 45 with x: -1.8894708936096978,y : 1.259647262406465\n",
      "iterator 46 with x: -1.8705761846736009,y : 1.2470507897824004\n",
      "iterator 47 with x: -1.8518704228268648,y : 1.2345802818845764\n",
      "iterator 48 with x: -1.8333517185985961,y : 1.2222344790657307\n",
      "iterator 49 with x: -1.8150182014126102,y : 1.2100121342750734\n",
      "iterator 50 with x: -1.796868019398484,y : 1.1979120129323226\n",
      "iterator 51 with x: -1.7788993392044992,y : 1.1859328928029995\n",
      "iterator 52 with x: -1.7611103458124542,y : 1.1740735638749695\n",
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      "iterator 56 with x: -1.6917155713571637,y : 1.127810380904776\n",
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      "iterator 59 with x: -1.6414699271722846,y : 1.0943132847815231\n",
      "iterator 60 with x: -1.6250552279005617,y : 1.0833701519337078\n",
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      "iterator 66 with x: -1.5299572387486968,y : 1.0199714924991312\n",
      "iterator 67 with x: -1.51465766636121,y : 1.00977177757414\n",
      "iterator 68 with x: -1.4995110896975978,y : 0.9996740597983985\n",
      "iterator 69 with x: -1.484515978800622,y : 0.9896773192004146\n",
      "iterator 70 with x: -1.4696708190126158,y : 0.9797805460084105\n",
      "iterator 71 with x: -1.4549741108224896,y : 0.9699827405483263\n",
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      "iterator 73 with x: -1.4260201260171221,y : 0.9506800840114147\n",
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      "iterator 78 with x: -1.3561309507994272,y : 0.9040873005329515\n",
      "iterator 79 with x: -1.342569641291433,y : 0.895046427527622\n",
      "iterator 80 with x: -1.3291439448785187,y : 0.8860959632523457\n",
      "iterator 81 with x: -1.3158525054297336,y : 0.8772350036198223\n",
      "iterator 82 with x: -1.3026939803754363,y : 0.8684626535836241\n",
      "iterator 83 with x: -1.289667040571682,y : 0.8597780270477878\n",
      "iterator 84 with x: -1.2767703701659652,y : 0.85118024677731\n",
      "iterator 85 with x: -1.2640026664643056,y : 0.8426684443095369\n",
      "iterator 86 with x: -1.2513626397996624,y : 0.8342417598664416\n",
      "iterator 87 with x: -1.2388490134016659,y : 0.8258993422677772\n",
      "iterator 88 with x: -1.2264605232676493,y : 0.8176403488450994\n",
      "iterator 89 with x: -1.2141959180349728,y : 0.8094639453566485\n",
      "iterator 90 with x: -1.202053958854623,y : 0.801369305903082\n",
      "iterator 91 with x: -1.1900334192660769,y : 0.7933556128440512\n",
      "iterator 92 with x: -1.1781330850734162,y : 0.7854220567156107\n",
      "iterator 93 with x: -1.166351754222682,y : 0.7775678361484546\n",
      "iterator 94 with x: -1.1546882366804552,y : 0.7697921577869701\n",
      "iterator 95 with x: -1.1431413543136506,y : 0.7620942362091003\n",
      "iterator 96 with x: -1.131709940770514,y : 0.7544732938470093\n",
      "iterator 97 with x: -1.1203928413628088,y : 0.7469285609085392\n",
      "iterator 98 with x: -1.1091889129491808,y : 0.7394592752994538\n",
      "iterator 99 with x: -1.098097023819689,y : 0.7320646825464592\n",
      "stop in 798 interations\n",
      "after updating x is -0.0009862943461286678, y is 0.0009828958482367542\n"
     ]
    }
   ],
   "source": [
    "for i in range(0, epoch):\n",
    "    stop_x = False\n",
    "    stop_y = False\n",
    "    if abs(prev_x - x) < precision:\n",
    "        stop_x = True\n",
    "    else:\n",
    "        prev_x = x\n",
    "        x = x - r * (x)\n",
    "    if abs(prev_y - y) < precision:\n",
    "        stop_y = True\n",
    "    else:\n",
    "        prev_y = y\n",
    "        y= y- r * (y)\n",
    "    if stop_x and stop_y:\n",
    "        print(\"stop in {0} interations\".format(i))\n",
    "        break\n",
    "    if i < 100:\n",
    "        print(\"iterator {0} with x: {1},y : {2}\".format(i, x, y))\n",
    "\n",
    "print(\"after updating x is {0}, y is {1}\".format(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "8 "
   ]
  }
 ],
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